Ethernet and wi-fi simultaneously on my Mac

As Barney said, you can activate both Ethernet and WiFi for your Mac. Then open Network Preferences and you will see this.

(Yours should show both Ethernet and WiFi as "connected" with green dots for both)

Click on the circle with three dots in it (just to the right of the + and - options) and set the order for that Mac to use Ethernet first. It will be connected to WiFi also but will use Ethernet for its internet. Other computers can use WiFi.

To which device do you have your Mac's wired ethernet connected (Virgin Media vs. TP-LInk)?

If your layout is as follows then you should connect your Mac to one of the gigabit ports on the TP Link device:

Internet service provider <--> Virgin Media device in modem mode <--> TP Link mesh device <--> in-home network

Also,

WiFI should be turned off in the Virgin Media device (only the TP Link Mesh unit should be serving WiFi)

All client devices (wired & WiFI) should connect to the TP Link device

Which of the 2 devices do you have acting as your DHCP server? It should not be both.

Are they the same network? There should be no problem using Ethernet and Wi-Fi at same time.